Score : $200$ points

Problem Statement

You are given a image with a height of $H$ pixels and a width of $W$ pixels. Each pixel is represented by a lowercase English letter. The pixel at the $i$-th row from the top and $j$-th column from the left is $a_{ij}$.

Put a box around this image and output the result. The box should consist of # and have a thickness of $1$.

Constraints

• $1 \leq H, W \leq 100$
• $a_{ij}$ is a lowercase English letter.

Input

Input is given from Standard Input in the following format:

$H$ $W$

$a_{11}$ $...$ $a_{1W}$

$:$

$a_{H1}$ $...$ $a_{HW}$

Output

Print the image surrounded by a box that consists of # and has a thickness of $1$.

2 3
abc
arc

#####
#abc#
#arc#
#####

1 1
z

###
#z#
###